Statistical Modelling of Cell Cycle Dynamics

Sara Larsson

Centre for Mathematical Sciences
Mathematical Statistics
Lund University

ISBN 978-91-628-7119-2

It is of great importance to increase the knowledge of various cell cycle kinetic parameters and the objective of this thesis is to use stochastic models to interpret Bromodeoxyuridine (BrdUrd) DNA Flow Cytometry (FCM) derived data in order to estimate such parameters. The cell cycle is the process of growth and division that is essential for an organism to increase in size. The cell cycle consists of several consecutive phases and one of these is the S phase, during which DNA is duplicated. The duration of this phase is the main focus of the thesis although the following G2 phase is also studied. Most of the previous methods developed to estimate the duration of the S phase consider its length as a deterministic value. The variation within a cell population is large though and to obtain information regarding the variation in S phase duration it is necessary to consider stochastic models.
When using the BrdUrd DNA FCM method the DNA content can be measured under certain circumstances and the DNA distribution of cells followed through the cell cycle. Cells in S phase are labelled with BrdUrd and it is the DNA content in this subpopulation of cells that is measured at various times after BrdUrd labelling.
In the first place, the models considered in this thesis are based on asymptotic results from branching processes. To obtain information regarding the duration of the S phase it is crucial to have a model for the rate at which DNA is duplicated. There is no parametric model known to describe this rate and therefore nonparametric approaches are proposed. Furthermore, the duration of the S phase is assumed to be gamma distributed, resulting in an expression for the progression of the DNA distribution over time. The derived expression is then compared with the obtained data. However, there is also a measurement variation which has to be modelled. Different approaches are investigated; a deconvolution approach and including the measurement variation in the likelihood.
The estimated durations of the S phase and the G2 phase turn out to be rather large, strengthening the importance of considering stochastic models when modelling cell cycle dynamics.
Key words:
Branching processes, cell cycle kinetics, DNA distribution, S phase duration, G2 phase duration, DNA replication, flow cytometry,